# Showing papers in "The American Statistician in 1967"

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95 citations

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TL;DR: In the course of its studies of business cycles, the National Bureau of Economic Research has identified successive periods of business expansion and contraction in the United States and several other countries as discussed by the authors.

Abstract: In the course of its studies of business cycles, the National Bureau of Economic Research has identified successive periods of business expansion and contraction in the United States and several other countries. Business cycle peak dates mark the end of a period of expansion and the beginning of a period of contraction; trough dates mark the end of a period of contraction and the beginning of a period of expansion. For the United States the chronology goes back to 1854 on a monthly and quarterly basis, and to 1834 on an annual basis. Between 1854 and 1961 (the last trough date) some 26 peaks and 27 troughs have been recognized. These dates identify 26 expansions and 26 contractions. The 10 contractions since 1920 are recorded in Table 1.

53 citations

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TL;DR: In this article, it was observed that the corresponding series of polyhedral arrays provided iminimum location designs for rlh order polynomials in k variables. But it does not appear to have been observed that these arrays can be constructed as an allocation problem as in the following example.

Abstract: It is well known that the k-dimension simnplex (Triangle, Tetrahedron, etc.) provides a minimum location design for a first order polynomial in k variables. It does not appear to have been observed that the corresponding series of polyhedral arrays provide iminimum location designs for rlh order polynomials in k variables. If we label one set of diagonals in Pascal's triangle as the number of variables and the other set as the order of the polynomial then the intersection of the k and r diagonals gives the polyhedral array for the rtll order polynomial in k variables. Design coordinates can be conveniiently constructed as an allocation problem as in the following example. The permutations of each allocation provide the coordinates of the design locations. Example: 4th Order in 4 Variables Allocation Permutations

41 citations

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TL;DR: Several aspects of the disparity in birth ratio of males over females are discussed including variations among different races, variations by order of birth, by age of the parent, and in multiple births.

Abstract: Several aspects of the disparity in birth ratio of males over females are discussed including variations among different races variations by order of birth by age of the parent and in multiple births. Avenues of statistical exploration are suggested in an attempt to indicate certain peculiarities in nature. The Negro population in the United States has a sex ratio of 102 males to 100 females as opposed to 105:100 for whites a highly significant difference. Inferences from these statistics are suggested for study of the sex ratios of mixed unions. The group classified as Mulatto show a lower sex ratio and further analysis of this was suggested including examination of slave records. For the white population sex ratio declines from 106.2 to 102.9 between 1st order and 7th order births. This is highly significant. However nonwhite determinations were more irregular. Data limitations on sex ratio by age of parent prevented conclusive results. Multiple births among whites show a decline from 105.3 for single live births to 103.2 for twins and 86.1 for all other plural deliveries. Among nonwhites these ratios are 102.3 99.7 and 102.6 respectively. Further information should be developed using the multiple facts relating to the sex ratio at birth.

37 citations

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TL;DR: For specified values of v and the sample size, table 1 presents upper limits for estima-tes of v that will still result in MSE (y') being less than the variance of y.

Abstract: Since (3) is ait upward c(uadratic functioni of W47 there are at most two imitersectioti poinlts with a line representinig 72/tn (as itndicated above.) One initersectioni takes place at C2 = 0 anid there is ino other when 71 < 112 sinice in this case eveii if C2 = co , AIISE (y') is still less tlhani U2/ . For specified values of v and the sample size, table 1 presents upper limits for estima-tes of v that will still result in MSE (y') being less thlani the variance of y. Wlhile the results for all sizes of v are of interest the gains are smiall wlheni v is less than onie.

28 citations

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TL;DR: In this paper, the authors make a distinction between the short-run and the long-run in the evaluation of this problem and make a treatment of this issue along this time path, in two progressions: from the particular to the general and from the short run to the long run.

Abstract: During the time that this report was under review by the Administration it became "caught up" in a substantial public controversy over the alleged threat to personal privacy embodied in its recommendations. The report and the Administration's intentions were made the object of hearings before the subcommittees of Senator Long of Missouri in the Senate and Congressman Gallagher of New Jersey in the House. Through extensive comment in the public press, the report acquired the image of a design to establish a gargantuan centralized national data center calculated to bring Orwell's "1984" at least as close as 1970. It is the theme of this paper that the image embodied in the "purple phrases" that characterized the public reports do not reflect either the realities of the proposals or the balance that Congressman Gallagher and Senator Long attempted to bring to this issue in the hearings. The author wishes to take this means of correcting certain obvious misinterpretations and set forth more explicitly some views on the very important issue of personal privacy. The topic will be presented in two progressions: from the particular to the general and from the short run to the long-run. We must start with the particular: the author's report to the Bureau of the Budget and then move to a more general perspective of the issue. Because of the overriding importance of realistic time dimensions in the evaluation of this problem we also need to make a distinction between the short-run and the long-run and we shall progress, in our treatment, along this time path. (It will help to bear in mind that the author's concept of the short-run implies something like ten to fifteen years.) The treatment of this issue in the press and in public hearings has coilfused the particular and the general and the short-run and the long-run. We will begin by reviewing briefly what the "Dunn report" does and does not say. First, contrary to reports, it does not constitute a formal plan in any sense. It is primarily an informal review of certain problems and prospects associated with the management and organization of statistical inforrnation generated by public, general-purpose statistical programs within the federal government. It was a preliminary review carried out with limited time and resources. The conclusions of this review were circulated within various administrative agencies as a basis for discussion and taken for evaluation by the administration. The report did state that certain obstacles to effective use of federal statistical files might require some centralization of function. It did not at any point recommend what changes should be made or what agencies or files should be involved. It contented itself with a generalized treatment of the problem and some indication of the general direction in which the solutions might lie. It was not presented as a final program design.

26 citations

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TL;DR: In this paper, a single sample problem with two observations on each element in the sample, analogous to a paired sample problem, is considered, where two factors or attributes may be either present or absent in the observations in a sample, and one wishes to determine the strength of the relationship between the factors, available correlation techniques for nominal data do not seem to apply.

Abstract: Where two factors or attributes may be either present or absent in the observations in a sample, and one wishes to determine the strength of the relationship between the factors, available correlation techniques for nominal data do not seem to apply. Here we have a single sample problem, but two observations on each element in the sample, analogous to a paired sample problem. The data can be recorded as tl where the factor is present, and -1 if the factor is absent. If the factors are either both present or both absent in the ith observation pair (Xi, Y,) so that there is agreement, then xi - Y, = 0 , and \Xi - Y,I = 2 for disagreement,

22 citations

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TL;DR: The author is not familiar with any application of the principle of sig,nificant inconsistency to actual wagering, and the returns given in this report are entirely hypothetical.

Abstract: F(0717p)=-p4+4(1 p)p4 +10 (I -p)2p-'. After one victory, we have F(1,O,p)-p3?3(1-p)p3?6(1-p) 2p3?1(1-p) 3p3. For other situations, we have F(1,1,p) =p3+3( -p) p3+6(-p) 2p3, F(1,2,p) =p3+3(l-p) p3, F(2,1,p) =p2+2( -p) p2+3(l-p) 2p2, F (2,2,p) =p' + 2 (I -p) p2' F(2,3,p) = p29 F(3,2,p) =p9+ (I-p)p, F (3a3cp) =o p The application of the principle of sig,nificant inconsistency is demonstrated in Tables I and II. Odds quoted as AB mean that B dollars bet on Los Angeles would have netted A dollars if Los Angeles had won. In both examples a successful hedge could have been taken at the recommended time. If this had been impossible, one would have had to split bets for another round, and sometimes even until the bitter end. Notice that one-sided inconsistencies in the odds may persist over long time periods. For several games in a row during the 1965 series, both in Minnesota and in Los Angeles, the Las Vegas odds on Los Angeles for a game implied higher series odds than those actually reported. The author is not familiar with any application of this system to actual wagering, and the returns given in this report are entirely hypothetical.

21 citations

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TL;DR: The Teacher's Corner: An Inequality Satisfied by the Expectation of the Reciprocal of a Random Variable as mentioned in this paper is a classic example of a teacher's corner book.

Abstract: (1967). The Teacher's Corner: An Inequality Satisfied by the Expectation of the Reciprocal of a Random Variable. The American Statistician: Vol. 21, No. 2, pp. 24-25.

21 citations

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TL;DR: In this paper, the authors pointed out that Shaw's criticism of the use of graphic correlation may spring from a lack of experience with the method and of appreciation of the mathematical principle it is based on.

Abstract: and of the effects of weather). Shaw's criticism of the use of graphic correlation may spring from a lack of experience with the method and of appreciation of the mathematical principle it is based on. I suspect this from his various comments including his questioning my use of .16 bushels increase for every one percent of acreage seeded with hybrid seed. This figure happens to be practically the same (.18) Shaw and Durost found in the multiple correlation results by computer, in USDA-AE Report 80. It perhaps should also be pointed out, in view of Shaw's footnote 16, that in calling attention to differences in results by the same authors (Shaw and Durost) using different methods in a later study, I was comparing differences in trends in technology effects in the several recent decades and not differences in year to year weather effects as measured by weather indexes. I must therefore plead "not guilty" to the charges that I made "year to year comparisons" and that "comparisons such as those by Bean are illegitimate uses of the weather index".

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TL;DR: The purpose of this paper is to report the progress of a formal program adopted by the editorial board of one scientific journal aimed at improving the quality of the research reported in its pages.

Abstract: The editorial staffs of many scientific journals hold the authors of submitted manuscripts responsible for the research designs of their studies, the applicability of the statistical tests used, and the validity of the conclusions drawn. The investigators in many cases have had very little, if any, training in research methods. The purpose of this paper is to report the progress of a formal program adopted by the editorial board of one such scientific journal aimed at improving the quality of the research reported in its pages.

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TL;DR: In this article, a brief recognition is given to bicentennials of the death of James Stirling (1692-1770) and birth of Ferdinand Rudolph Hassler (1770-1843).

Abstract: Brief recognition is given to bicentennials of the death of James Stirling (1692–1770) and birth of Ferdinand Rudolph Hassler (1770–1843); to sesquicentennials of the publication of the 3rd definitive edition of Laplace's Theorie analytique des probabilites, and of the births of William Chauvenet (1820–1870) and Isaac Todhunter (1820–1884); to centennials of the births of Louis Bachelier (1870–1946) and Jean Perrin (1870–1942); and to the semicentennial of the initial publication (1920) of Metron, an International Review of Statistics.

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TL;DR: In this paper, the authors show that if a random variable Y has a nondegenerate increasing (dec.) r egression E(YIX) on a non-degenerate random variable X, then X and Y have positive covatriance.

Abstract: E(XJ ) > (EX)-1 (1) for a non-degenerate positive random variable X. Fleiss [2] gave a simple proof, in pedagogic interest, and an application. Chian, [1] contributed a simpler proof. Finally, Gurland [3] gave a still simpler argument and obtained in the same stroke a wider result. The present note (a) attaches intuitive meaning to these results by exhibiting them as consequences of an obvious property of covariance and (b) proves the property by the same device used in [3]. Thus, while retaining the simplicity achieved in [3], we can gain further generality and, more importantly, augment the intuitive basis implicit there. The property is: If a random variable Y has a nondegener-ate increasing (dec.) r egression E(YIX) on a non-degenerate random variable X, then X and Y have positive (neg.) covatriance. Putting Y X-'= E(YIX), we have 0 > Cov [X,Y] I E(X) E(X-'), which is (1). Again, putting X= J(Z), Y = g(Z) for a nondegenerate random variable Z and monotone functions / and g, one of which is continuous, the main result of [3] is given. A simple argument proves the property. The function q(x) = E(YIX = x) EY is monotone and Eq(X) = 0, so there is a point 4 at which q (x) either becomes zero or changes sign. Then the random variable (X-4)q(X) cannot change sign and moreover E(X-4)q(X) =A 0 since neither X nor q (X) is degenerate. In view of

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TL;DR: In this paper, the authors apply some of the current methodology and thinking of operations research to an analysis of the cumulative flow of water in the bathtub and present an extension of a paper that recently appeared in this journal.

Abstract: This paper applies some of the current methodology and thinking of operations research to an analysis of the cumulative flow of water in the bathtub. The analysis presented herein is an extension of a paper that recently appeared in this journal, viz. Operations Research at the Kitchen Sink and Other Applications.

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TL;DR: In this article, it is shown that by Schwarz's inequality for any two vectors, any convex function h(y) = \/y of a single real variable y can be replaced by a convex functions h(x, y) = x, y to obtain (1).

Abstract: of n real variables x1,x2,.. .xn, and use the fact that g (E(Xi), E (X2). I. . E (Xn) ) _< E(g(X-,X,,X. * .,X,,) ). to obtain (1) . Similarly consider the convex function h(y) = \/y of a single real variable y, use the fact n that h (E (Y)) E (h (Y) ), and replace Y by E X,2 to j 1 obtain (2). There is however a more elementary method for proving (1) and (2), which does not depend on the concept of convexity. It is as follows: By Schwarz's inequality for any two vectors

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TL;DR: Differential difference equations for decision procedure risk function based on noncentral chi squared and F distributions in multivariate statistical analysis as mentioned in this paper were used to evaluate the risk function of decision procedure.

Abstract: Differential difference equations for decision procedure risk function based on noncentral chi squared and F distributions in multivariate statistical analysis

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TL;DR: In this paper, the authors present the results of one of these attempts, particularly for those who are interested in general conclusions pertaining to agriculture beyond the controlled yield tests of the agricultural experiment stations.

Abstract: The Agricultural Revolution in the United States, the astonishing increase in productivity during the past 35 years, raises the question as to the relative contribution of technology and of weather. Several attempts have been made to answer this question and this paper presents the results of one of these attempts, particularly for those who are interested in general conclusions pertaining to agriculture beyond the controlled yield tests of the agricultural experiment stations.

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TL;DR: The early years of crop reporting in the U. S.S. were characterized by a significant amount of response error, which was identified as a major source of error in some early reports as mentioned in this paper.

Abstract: The Early Years . One hundred years .ago crop reporting was officially established in the U. S. Department of Agriculture by a $20,000 item in the Appropriation Act. The Depart. ment was then only four years old. Long before that time the need for statistical information was realized and limited efforts to supply it had been made, but it .was not until 1866 that USDA began issuing nationwide crop reports on a continuous basis. Data from the decennial ceDllUsesof agriculture, first taken in 1840, were basic to the calculation of esti· mates. Intercensal published reports were based upon inquiries sent to farmers, who were requested to an· swer for the localities with which they were familiar "rather than their farms, on the assumption that the wider coverage would provide more accurate results. The most important factors involved in selecting cor· respondents were evidently good geographic representa. tion and intelligent, literate farmers with ability to judge crop prospects and year-to·year changes. The inquiries requested information on acreage harvested and numbers of livestock as a "percentage of last year." Farmer reporters also were asked annually to give information on prices received for agricultural products and wages paid to farm laborers. Condition and yield per acre of crops were generally published as State and national averages of reporters' returns, as were prices and wage rates. Percentage changes in acreages of crope harvested and in numbers of livestock were published as reported or as adjusted together with the calculated estimates of State and na· tional totals. Very early in the history 'of crop and livestock reporting, the statistici8Dllrecognized response error as a major source of error in some iDlltances.A good exam· pIe was cash crop bias resulting from the tendency of the crop reporters to be over-conservativein reporting condition and yield per acre of crops grown for sale, especiallybefore much of the crop was sold. Parenthetically, it should be noted that census returns suffered from this same cash-crop bias, though to a lesser extent because CeDllUses were ordinarily taken at post-harvest and often post-sale dates. There was also an apparent failure of the year·to-year changes indicated by farmers' reports to reflect the rapid changes in crop acreages and livestock numbers that were taking place in the expanding agriculture of the period. The art of statistics was still in its infancy, as evidenced by statements issued with some early reports on such elemental matters as the definition of a weighted average

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